Properties

Label 4000.1.bo
Level 4000
Weight 1
Character orbit bo
Rep. character \(\chi_{4000}(257,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 24
Newforms 3
Sturm bound 600
Trace bound 37

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Defining parameters

Level: \( N \) = \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 4000.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 3 \)
Sturm bound: \(600\)
Trace bound: \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).

Total New Old
Modular forms 360 24 336
Cusp forms 40 24 16
Eisenstein series 320 0 320

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\(24q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4000.1.bo.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(D_{20}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots\)
4000.1.bo.b \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(D_{20}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots\)
4000.1.bo.c \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(D_{20}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)